simplify ln(75/49)

Solution

simplify

ln (\frac{75}{49})

ln (75) - 2 ln (7)

Decimal Notation

0.42566 \dots

Solution steps

ln (\frac{75}{49})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{75}{49}) = ln (75) - ln (49)

= ln (75) - ln (49)

ln (49) = 2 ln (7)

= ln (75) - 2 ln (7)

ln (ln (\frac{1}{1 - 0.02})) - ln (ln (\frac{1}{1 - 0.003}))

2.45 + lo g_{10} (\frac{0.022}{0.069})

(0.287) ln (\frac{500}{200})

2 lo g_{3} (2) - 3 lo g_{3} (4) - 2 lo g_{3} (5)

ln (19) - ln (44)